Acousto-optic devices and systems that incorporate them can be used to modulate optical beams. For example, acousto-optic modulators can be used to diffract an optical beam, thereby modulating the spatial intensity distribution and/or phase of the optical beam. Acousto-optic devices can also be combined with additional elements in order to produce further changes in one or more properties of the optical beam, such as changes in the frequency and/or polarization state of the optical beam. For example, acousto-optic devices can be used to produce, from an input beam, two linearly and orthogonally polarized output beams having frequencies that differ from a frequency of the input beam. Methods for generating linearly and orthogonally polarized optical beams from an input beam using an acousto-optic device are disclosed, for example, in U.S. Pat. No. 6,157,660 entitled “APPARATUS FOR GENERATING LINEARLY-ORTHOGONALLY POLARIZED LIGHT BEAMS” by Henry A. Hill, and in U.S. Pat. No. 6,236,507 entitled “APPARATUS TO TRANSFORM TWO NONPARALLEL PROPAGATING OPTICAL BEAM COMPONENTS INTO TWO ORTHOGONALLY POLARIZED BEAM COMPONENTS” by Henry A. Hill and Peter de Groot, the entire contents of both of which are incorporated herein by reference.
Acousto-optic devices can be incorporated into larger measurement systems. For example, an acousto-optic device configured to produce two linearly and orthogonally polarized output beams from an input beam can be incorporated into a displacement or dispersion measuring interferometry system. In such interferometry systems, the acousto-optic device can be used, for example, to generate measurement and reference beams to perform measurement functions. Displacement measuring interferometry systems that incorporate acousto-optic devices can be used, for example, to measure angular and linear displacements of objects such as a mask stage or a wafer stage in a lithography scanner or stepper system. Dispersion measuring interferometers that incorporate acousto-optic devices can be used, for example, to determine intrinsic properties of gases.
Displacement measuring interferometers monitor changes in the position of a measurement object relative to a reference object based on an optical interference signal. The interferometer generates the optical interference signal by overlapping and interfering a measurement beam reflected from the measurement object with a reference beam reflected from the reference object.
In many interferometry applications, the measurement and reference beams have orthogonal polarizations and different frequencies. The orthogonal polarizations allow a polarizing beam-splitter to direct the measurement and reference beams to the measurement and reference objects, respectively, and to combine the reflected measurement and reference beams to form overlapping exit measurement and reference beams. The overlapping exit beams form an output beam that subsequently passes through a polarizer. The polarizer mixes polarizations of the exit measurement and reference beams to form a mixed beam. Components of the exit measurement and reference beams in the mixed beam interfere with one another so that the intensity of the mixed beam varies with the relative phase of the exit measurement and reference beams. A detector can be configured to measure a time-dependent intensity of the mixed beam and to generate an electrical interference signal proportional to that intensity. Because the measurement and reference beams have different frequencies, the electrical interference signal includes a “heterodyne” signal having a beat frequency equal to the difference between the frequencies of the exit measurement and reference beams. If the lengths of the measurement and reference paths are changing relative to one another, e.g., by translating a stage that includes the measurement object, the measured beat frequency includes a Doppler shift equal to 2vnp/λ, where v is the relative speed of the measurement and reference objects, λ is a nominal wavelength of the measurement and reference beams, n is the refractive index of the medium through which the light beams travel, e.g., air or vacuum, and p is the number of passes to the reference and measurement objects. Changes in the relative position of the measurement object correspond to changes in the phase of the measured interference signal, with a 2π phase change corresponding to a distance change L of λ/(np), where L is a round-trip distance change, e.g., the change in distance to and from a stage that includes the measurement object.
In dispersion measuring applications, optical path length measurements are made at multiple wavelengths, e.g., 532 nm and 1064 nm, and are used to measure dispersion of a gas in the measurement path of a distance measuring interferometer. The dispersion measurement can be used to convert the optical path length measured by the distance measuring interferometer into a physical length. Such a conversion can be important since changes in the measured optical path length can be caused by gas turbulence and/or by a change in the average density of the gas in the measurement arm of the interferometer, even though the physical distance to the measurement object is unchanged. In addition to the extrinsic dispersion measurement, the conversion of the optical path length to a physical length requires knowledge of an intrinsic value of the gas. The factor Γ is a suitable intrinsic value and is the reciprocal dispersive power of the gas for the wavelengths used in dispersion interferometry. The factor Γ can be measured separately or can be based on literature values.
Unfortunately, imperfections in the interferometry system can degrade the accuracy of such interferometric measurements. For example, many interferometers include non-linearities such as what are known as “cyclic errors.” The cyclic errors can be expressed as contributions to the phase and/or the intensity of the measured interference signal and have a sinusoidal dependence on phase changes associated with changes in optical path length pnL and/or on phase changes associated with other parameters. In particular, there is first harmonic cyclic error in phase that has a sinusoidal dependence on (2πpnL)/λ and there is second harmonic cyclic error in phase that has a sinusoidal dependence on 2 (2πpnL)/λ. Higher harmonic cyclic errors may also be present.
Other types of errors in interferometry systems include wavefront errors, which can arise, for example, from imperfections in relay optics used to transport an optical beam from a source to an interferometer, and from imperfections in interferometer and detector optics. Wavefront errors can also lead to errors in phase measurements in interferometry systems. Methods for reducing wavefront errors in interferometry systems are disclosed, for example, in U.S. Pat. No. 6,727,992 B2 entitled “METHOD AND APPARATUS TO REDUCE EFFECTS OF SHEARED WAVEFRONTS ON INTERFEROMETRIC PHASE MEASUREMENTS” by Henry A. Hill, the entire contents of which are incorporated herein by reference.
In interferometry systems that incorporate acousto-optic devices, wavefront errors can also arise from diffraction effects within the acousto-optic device. In general, acousto-optic devices can be configured to modulate an optical beam by directing the optical beam to interact with an acoustic wave in an acoustic cell. For example, an optical beam can undergo diffraction in a region of the acousto-optic cell that includes the acoustic wave. The wavefront figures of both undiffracted (i.e., zero-order) and diffracted beams can be modulated in the acousto-optic device, and the amplitude and/or phase of the modulation can be different at different transverse spatial positions within the cross-sectional profile of the optical beams.
The effect of wavefront errors will depend upon procedures used to mix components of the output beam with respect to component polarization states and to detect the mixed output beam to generate an electrical interference signal. The mixed output beam can for example be detected by a detector without any focusing of the mixed beam onto the detector, by detecting the mixed output beam as a beam focused onto a detector, or by launching the mixed output beam into a single mode or multi-mode optical fiber and detecting a portion of the mixed output beam that is transmitted by the optical fiber. The effect of wavefront errors will also depend on properties of a beam stop should a beam stop be used in the procedure to detect the mixed output beam. Generally, the errors in the interferometric signal are compounded when an optical fiber is used to transmit the mixed output beam to the detector.